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Why are there moving lights at the bottom of swimming pools? Here comes the Transport of Intensity effect.

Have ever noticed this typical network of bright-and-dark areas on the bottom of a swimming pool? You certainly observed that its variations were correlated to how much the water was agitated by swimmers or divers. But why does this happen? And how can we use this for scientific applications? Let me show you. Why do water waves generate a bright and dark network in the swimming-pool Here is a simplified illustration of the phenomenon using geometrical optics: